Certification of high-dimensional entanglement in ultracold atom systems

Preparing strongly entangled quantum states with high confidence is a key requirement for the implementation of uprising quantum technologies, like quantum encryption protocols. To certify the entanglement available in any prepared state, reliable methods for its experimental detection are needed. One such method has been introduced recently and demonstrated with entangled photon pairs [J. Bavaresco, Nature Physics 2018], allowing one to extract the entanglement dimension, a measure for bipartite entanglement. In cold-atom systems, which represent the most advanced platform for quantum simulation, these methods cannot be applied directly due to limited readout capabilities. Here we present an adaptation of the scheme to ultracold atoms in optical lattices utilizing measurements in two experimentally accessible bases and study its robustness with respect to experimental imperfections and noise. We also extend the method to multipartite systems, enabling the certification of genuine tripartite entanglement.